The English defeated South Africa by an innings and 53 runs at St George’s Park in Port Elizabeth on Monday.
England had been 4-148 on the first day before Ben Stokes (120) and Ollie Pope (135*) combined for a match-winning 203-run partnership.
The century was Pope’s first in Test cricket in his sixth match, and also earned him Player of the Match honours.
Dominic Bess took a five-wicket haul while Stuart Broad claimed 3-30 as the Proteas were rolled for 209 in their first innings.
Root enforced the follow-on and took four stunning second innings wickets himself, while Mark Wood took three scalps as well as South Africa were bowled out for 237, unable to make the tourists bat again.
England, who drew 2-2 with Australia in last year’s Ashes on home turf, have clawed their way back from 1-0 down in the South Africa series to win the next two matches.
The result earns England 30 points in the ICC World Test Championship. England are currently ranked fifth on the ICC Test Rankings but Root is dreaming of top spot again.
“It’s not going to happen overnight, there’s going to be bumps in the road,” Root said.
“As long as the group is willing to learn and put the work in time and time again doing the things that aren’t necessarily the most flattering, the quite difficult things to do in Test cricket then we’ll be fine.
“That’s why we won the game in Cape Town, because throughout that whole last session, at no stage did we not think were going to win that Test.
“That’s the sort of attitude you need consistently if you want to keep improving and want to get to No.1 in the world.
“If we can harness that like we did this week, then well start to be more consistent.”
The Fourth and final Test match between England and South Africa takes place from Friday at Wanderers in Johannesburg.